The difference in responsibility between a head coach and their assistants is often understated in hockey discourse.
A head coach is the master of their domain in the most literal sense of the term. They oversee everything even remotely related to the team – from the minutiae of systems work, to lineup decisions, to a facet as seemingly ancillary as the practice schedule.
If the team is the body, the head coach is, well, the head. Hence; the name.
Assistants, on the other hand, handle duties which are much more specific. They typically oversee tasks such as the special teams configuration, along with dictating the mid-game usage of either positional group, and more or less acting as a conduit between the players and the head coach on both a personal and professional level.